

Naming Polynomials
Presentation
•
Mathematics
•
8th Grade
•
Hard
James Gonzalez
FREE Resource
8 Slides • 22 Questions
1
Introduction to Polynomials
Target: Identify the degree and lead coefficient of a given polynomial.
2
A math expression containing two or more algebraic terms
Ex: 4x5 + 2x4 - 3x3 + 8x2 + 7x - 10
Polynomials Definition
3
Simply: rearrange the terms of the polynomial so the largest exponent is first, and the smallest exponent is last
10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 -2 - 1
Let's talk descending order
4
STANDARD FORM of a POLYNOMIAL
all of the terms are in order from highest degree to the lowest degree.
EXAMPLE
Write in STANDARD FORM
5y2 + w4 + w7 - q3 + 2y - 10
5
Multiple Choice
Which answer properly places the polynomial in the correct descending order?
6x2+7x4+5x3+15−8x
7x4−8x+6x2−5x3+15
5x3+7x4−8x+6x2+15
15−8x+7x4+6x2+5x3
7x4+5x3+6x2−8x+15
6
Multiple Choice
Which answer properly places the polynomial in the correct descending order?
9x5−3x2+8x−18
9x5−3x2+8x−18
−3x2+8x−18+9x5
−18+9x5−3x2+8x
−18+9x5+8x−3x2
7
The degree of a polynomial is determined by the LARGEST exponent.
This is why its beneficial to put into descending order.
Some text here about the topic of discussion.
Degrees of Polynomials
8
Multiple Choice
What is the degree of the polynomial
7x4−8x6+2x2−10
4
6
2
0
9
Multiple Choice
What is the degree of the polynomial
10x3−7x2+9x5−x8+7
3
2
5
8
10
Based on the degree of the polynomial, we can assign a name to that polynomial
Names are shown to the left
Names of Polynomials
11
Multiple Choice
What is the name of the polynomial shown?
7x3+5x2−8x+10
Cubic
Quartic
Quadratic
Zero
12
Multiple Choice
What is the name of the polynomial shown?
−3x5+8x2−10+7x−4x3
Cubic
7th degree Polynomial
Quintic
Zero
13
The number of terms will create a classification for each polynomial
ex: 3 terms = trinomial
Naming Polynomials based on the number of terms
14
Multiple Choice
Name the following polynomial
5x2+2x−10
Monomial
Binomial
Trinomial
Polynomial with degree of 0
15
Multiple Choice
Name the following polynomial
−3x4+6x
Monomial
Binomial
Trinomial
Polynomial with degree of 0
16
Multiple Choice
Name the following polynomial
7x3y2
Monomial
Binomial
Trinomial
Polynomial with degree of 0
17
Multiple Choice
Name the polynomial and the number of terms
8x2+6x−16
Trinomial with 3 terms
Binomial with 2 terms
Polynomial with 4 terms
Monomial with 2 terms
18
Multiple Choice
Name the polynomial and the number of terms
−12x4
Trinomial with 3 terms
Binomial with 2 terms
Polynomial with 4 terms
Monomial with 1 term
19
Multiple Choice
Name the polynomial by degrees and number of terms
5x4+8x2−10x
Polynomial, 4 degrees, 3 terms
Binomial, 4 degrees, 2 terms
Monomial, 4 degrees, 1 term
Trinomial, 4 degrees, 3 terms
20
Multiple Choice
Name the polynomial by degrees and number of terms
10x3+7x2
Polynomial, 3 degrees, 2 terms
Binomial, 4 degrees, 2 terms
Trinomial, 4 degrees, 2 terms
Monomial, 4 degrees, 1 term
21
Multiple Choice
Write the following polynomial in descending order in terms of b
b3−a2b+4ab4−10a
4ab4+b3−a2b−10a
−10a+4ab4−a2b+b3
−a2b−10a+4ab4+b3
22
Multiple Select
Choose all the binomial expressions.
-5x + 12
2x2
2y2 - 2y + 2
19 - 7y
3x3 - 3
23
Multiple Choice
Name the polynomial by its degree.
3x2+7x−8
constant
linear
quadratic
cubic
24
Multiple Select
Chose all the descriptions that describe the polynomial.
−2x2−7
trinomial
linear
quadratic
binomial
monomial
25
Naming Polynomials
This isn't too important to memorize, but we will use some of this vocabulary such as binomial and trinomial in the future.
The degree is the highest exponent in the polynomial.
26
Multiple Choice
Classify by number of terms:
3x2 – 8x + 1
Monomial
Binomial
Trinomial
4-Term Polynomial
27
Multiple Choice
9x
28
Multiple Choice
Classify by number of terms:
3x3 – 6x
Monomial
Binomial
Trinomial
4-Term Polynomial
29
Multiple Choice
Classify the polynomial:
14x3+x2−x+2
Quadratic trinomial
Triad
Cubic
Fourth degree polynomial
30
Multiple Choice
Write the polynomial in standard form:
7x3−11x+x5−2
−11x+7x3−2+x5
x5+7x3−11x−2
7x3−11x+x5−2
18x5−2
Introduction to Polynomials
Target: Identify the degree and lead coefficient of a given polynomial.
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